On the Harmonic Oscillation of High-order Linear Time Invariant Systems

TL;DR

This paper investigates conditions for harmonic oscillation in high-order LTI systems and proposes a design method to control such oscillations, demonstrated through a fourth-order system example.

Contribution

It introduces a novel design procedure for controlling harmonic oscillations in high-order LTI systems using linear equations for system coefficients.

Findings

Derived sufficient conditions for harmonic oscillation.

Presented a design method for high-order LTI systems.

Demonstrated control of oscillations with example analysis.

Abstract

Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study investigates sufficient conditions to obtain harmonic oscillation for high-order LTI systems. The paper presents a design procedure for controlling harmonic oscillation of singleinput single-output high-order LTI systems. LTI system coefficients are calculated by the solution of linear equation set, which imposes a stable sinusoidal oscillation solution for the characteristic polynomials of LTI systems. An example design is demonstrated for fourth-order LTI systems and the control of harmonic oscillations are discussed by illustrating Hilbert transform and spectrogram of oscillation signals.